Chapter 4 Summary Scatter diagrams of data pairs (x, y) are useful in helping us determine visually if there is any relation between x and y values and,

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Presentation transcript:

Chapter 4 Summary Scatter diagrams of data pairs (x, y) are useful in helping us determine visually if there is any relation between x and y values and, if so, how strong the relation might be. We call x the explanatory variable and y the response variable. Chapter 4 Summary / 1

Summary cont. The correlation coefficient r gives a numerical measurement assessing the strength of a linear relationship between two variables x and y based on a random sample of data pairs (x, y). The value of r ranges from -1 to 1, with 1 indicating perfect positive linear correlation, -1 indicating perfect negative linear correlation and 0 indicating no linear correlation. The closer the sample statistic r is to 1 or -1, the stronger the linear correlation. Chapter 4 Summary / 2

Summary cont. If the scatter diagram and the correlation coefficient r indicate a linear relationship, then we use the least-squares criterion to develop the equation of the least-squares line between the explanatory variable x and the response variable y Where is the value of y predicted by the least-squares line, a is the y-intercept and b is the slope. The coefficient of determination is a value that measures the proportion of variation in y explained by the least-squares line. Chapter 4 Summary / 3